{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZkIHkjDWgySK"
      },
      "source": [
        "##### Copyright 2018 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "G5eriUZ9g1Ia"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iCUZvZvBB7VD"
      },
      "source": [
        "# Linear Mixed Effects Models\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Linear_Mixed_Effects_Models\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Models.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Models.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/Linear_Mixed_Effects_Models.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yDCkuCjq2DfW"
      },
      "source": [
        "A linear mixed effects model is a simple approach for modeling structured linear relationships (Harville, 1997; Laird and Ware, 1982). Each data point consists of inputs of varying type—categorized into groups—and a real-valued output. A linear mixed effects model is a _hierarchical model_: it shares statistical strength across groups in order to improve inferences about any individual data point.\n",
        "\n",
        "In this tutorial, we demonstrate linear mixed effects models with a real-world example in TensorFlow Probability. We'll use the JointDistributionCoroutine and Markov Chain Monte Carlo (`tfp.mcmc`) modules."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uiR4-VOt9NFX"
      },
      "source": [
        "### Dependencies & Prerequisites\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "coUnDhkpT5_6"
      },
      "outputs": [],
      "source": [
        "#@title Import and set ups{ display-mode: \"form\" }\n",
        "\n",
        "\n",
        "import csv\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import requests\n",
        "\n",
        "import tensorflow.compat.v2 as tf\n",
        "tf.enable_v2_behavior()\n",
        "\n",
        "import tensorflow_probability as tfp\n",
        "\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "\n",
        "dtype = tf.float64\n",
        "\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "%matplotlib inline\n",
        "plt.style.use('ggplot')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7nnwjUdVoWN2"
      },
      "source": [
        "### Make things Fast!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2CK9RaDcoYPG"
      },
      "source": [
        "Before we dive in, let's make sure we're using a GPU for this demo.\n",
        "\n",
        "To do this, select \"Runtime\" -> \"Change runtime type\" -> \"Hardware accelerator\" -> \"GPU\".\n",
        "\n",
        "The following snippet will verify that we have access to a GPU."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qP_4Xr8vpA42"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "SUCCESS: Found GPU: /device:GPU:0\n"
          ]
        }
      ],
      "source": [
        "if tf.test.gpu_device_name() != '/device:GPU:0':\n",
        "  print('WARNING: GPU device not found.')\n",
        "else:\n",
        "  print('SUCCESS: Found GPU: {}'.format(tf.test.gpu_device_name()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FJRBc_S0ppfE"
      },
      "source": [
        "Note: if for some reason you cannot access a GPU, this colab will still work. (Training will just take longer.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eikJTmPgB7VJ"
      },
      "source": [
        "## Data\n",
        "\n",
        "We use the `InstEval` data set from the popular [`lme4` package in R](https://CRAN.R-project.org/package=lme4) (Bates et al., 2015). It is a data set of courses and their evaluation ratings. Each course includes metadata such as `students`, `instructors`, and `departments`, and the response variable of interest is the evaluation rating."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lZ8OfS3cDMeG"
      },
      "outputs": [],
      "source": [
        "def load_insteval():\n",
        "  \"\"\"Loads the InstEval data set.\n",
        "\n",
        "  It contains 73,421 university lecture evaluations by students at ETH\n",
        "  Zurich with a total of 2,972 students, 2,160 professors and\n",
        "  lecturers, and several student, lecture, and lecturer attributes.\n",
        "  Implementation is built from the `observations` Python package.\n",
        "\n",
        "  Returns:\n",
        "    Tuple of np.ndarray `x_train` with 73,421 rows and 7 columns and\n",
        "    dictionary `metadata` of column headers (feature names).\n",
        "  \"\"\"\n",
        "  url = ('https://raw.github.com/vincentarelbundock/Rdatasets/master/csv/'\n",
        "         'lme4/InstEval.csv')\n",
        "  with requests.Session() as s:\n",
        "    download = s.get(url)\n",
        "    f = download.content.decode().splitlines()\n",
        "\n",
        "  iterator = csv.reader(f)\n",
        "  columns = next(iterator)[1:]\n",
        "  x_train = np.array([row[1:] for row in iterator], dtype=np.int)\n",
        "  metadata = {'columns': columns}\n",
        "  return x_train, metadata"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Um0EhvaDQcVI"
      },
      "source": [
        "We load and preprocess the data set. We hold out 20% of the data so we can evaluate our fitted model on unseen data points. Below we visualize the first few rows."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YY_VbNt6fkcp"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>students</th>\n",
              "      <th>instructors</th>\n",
              "      <th>studage</th>\n",
              "      <th>lectage</th>\n",
              "      <th>service</th>\n",
              "      <th>departments</th>\n",
              "      <th>ratings</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2819</th>\n",
              "      <td>114</td>\n",
              "      <td>104</td>\n",
              "      <td>8</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>11</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50715</th>\n",
              "      <td>2037</td>\n",
              "      <td>1031</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>11</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14934</th>\n",
              "      <td>585</td>\n",
              "      <td>926</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>59362</th>\n",
              "      <td>2406</td>\n",
              "      <td>739</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46935</th>\n",
              "      <td>1890</td>\n",
              "      <td>1084</td>\n",
              "      <td>6</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       students  instructors  studage  lectage  service  departments  ratings\n",
              "2819        114          104        8        5        0           11        4\n",
              "50715      2037         1031        2        2        0           11        5\n",
              "14934       585          926        4        1        1           10        4\n",
              "59362      2406          739        4        2        1            0        4\n",
              "46935      1890         1084        6        5        1           10        2"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data, metadata = load_insteval()\n",
        "data = pd.DataFrame(data, columns=metadata['columns'])\n",
        "data = data.rename(columns={'s': 'students',\n",
        "                            'd': 'instructors',\n",
        "                            'dept': 'departments',\n",
        "                            'y': 'ratings'})\n",
        "data['students'] -= 1  # start index by 0\n",
        "# Remap categories to start from 0 and end at max(category).\n",
        "data['instructors'] = data['instructors'].astype('category').cat.codes\n",
        "data['departments'] = data['departments'].astype('category').cat.codes\n",
        "\n",
        "train = data.sample(frac=0.8)\n",
        "test = data.drop(train.index)\n",
        "\n",
        "train.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qWttG6OaVFMO"
      },
      "source": [
        "We set up the data set in terms of a `features` dictionary of inputs and a `labels` output corresponding to the ratings. Each feature is encoded as an integer and each label (evaluation rating) is encoded as a floating point number."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NzfVQJN9B7VQ"
      },
      "outputs": [],
      "source": [
        "get_value = lambda dataframe, key, dtype: dataframe[key].values.astype(dtype)\n",
        "features_train = {\n",
        "    k: get_value(train, key=k, dtype=np.int32)\n",
        "    for k in ['students', 'instructors', 'departments', 'service']}\n",
        "labels_train = get_value(train, key='ratings', dtype=np.float32)\n",
        "\n",
        "features_test = {k: get_value(test, key=k, dtype=np.int32)\n",
        "                 for k in ['students', 'instructors', 'departments', 'service']}\n",
        "labels_test = get_value(test, key='ratings', dtype=np.float32)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "80ylfxWtB7VT"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of students: 2972\n",
            "Number of instructors: 1128\n",
            "Number of departments: 14\n",
            "Number of observations: 58737\n"
          ]
        }
      ],
      "source": [
        "num_students = max(features_train['students']) + 1\n",
        "num_instructors = max(features_train['instructors']) + 1\n",
        "num_departments = max(features_train['departments']) + 1\n",
        "num_observations = train.shape[0]\n",
        "\n",
        "print(\"Number of students:\", num_students)\n",
        "print(\"Number of instructors:\", num_instructors)\n",
        "print(\"Number of departments:\", num_departments)\n",
        "print(\"Number of observations:\", num_observations)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jMRMLuWwB7VX"
      },
      "source": [
        "## Model\n",
        "\n",
        "A typical linear model assumes independence, where any pair of data points has a constant linear relationship. In the `InstEval` data set, observations arise in groups each of which may have varying slopes and intercepts. Linear mixed effects models, also known as hierarchical linear models or multilevel linear models, capture this phenomenon (Gelman & Hill, 2006).\n",
        "\n",
        "Examples of this phenomenon include:\n",
        "\n",
        "+ __Students__. Observations from a student are not independent: some students may systematically give low (or high) lecture ratings.\n",
        "+ __Instructors__. Observations from an instructor are not independent: we expect good teachers to generally have good ratings and bad teachers to generally have bad ratings.\n",
        "+ __Departments__. Observations from a department are not independent: certain departments may generally have dry material or stricter grading and thus be rated lower than others.\n",
        "\n",
        "To capture this, recall that for a data set of $N\\times D$ features $\\mathbf{X}$ and $N$ labels $\\mathbf{y}$, linear regression posits the model\n",
        "\n",
        "$$\n",
        "\\begin{equation*}\n",
        "\\mathbf{y} = \\mathbf{X}\\beta + \\alpha + \\epsilon,\n",
        "\\end{equation*}\n",
        "$$\n",
        "\n",
        "where there is a slope vector $\\beta\\in\\mathbb{R}^D$, intercept $\\alpha\\in\\mathbb{R}$, and random noise $\\epsilon\\sim\\text{Normal}(\\mathbf{0}, \\mathbf{I})$. We say that $\\beta$ and $\\alpha$ are \"fixed effects\": they are effects held constant across the population of data points $(x, y)$. An equivalent formulation of the equation as a likelihood is $\\mathbf{y} \\sim \\text{Normal}(\\mathbf{X}\\beta + \\alpha, \\mathbf{I})$. This likelihood is maximized during inference in order to find point estimates of $\\beta$ and $\\alpha$ that fit the data.\n",
        "\n",
        "A linear mixed effects model extends linear regression as\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\eta &\\sim \\text{Normal}(\\mathbf{0}, \\sigma^2 \\mathbf{I}), \\\\\n",
        "\\mathbf{y} &= \\mathbf{X}\\beta + \\mathbf{Z}\\eta + \\alpha + \\epsilon.\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "where there is still a slope vector $\\beta\\in\\mathbb{R}^P$, intercept $\\alpha\\in\\mathbb{R}$, and random noise $\\epsilon\\sim\\text{Normal}(\\mathbf{0}, \\mathbf{I})$. In addition, there is a term $\\mathbf{Z}\\eta$, where $\\mathbf{Z}$ is a features matrix and $\\eta\\in\\mathbb{R}^Q$ is a vector of random slopes; $\\eta$ is normally distributed with variance component parameter $\\sigma^2$. $\\mathbf{Z}$ is formed by partitioning the original $N\\times D$ features matrix in terms of a new $N\\times P$ matrix $\\mathbf{X}$ and $N\\times Q$ matrix $\\mathbf{Z}$, where $P + Q=D$: this partition allows us to model the features separately using the fixed effects $\\beta$ and the latent variable $\\eta$ respectively.\n",
        "\n",
        "We say the latent variables $\\eta$ are \"random effects\": they are effects that vary across the population (although they may be constant across subpopulations). In particular, because the random effects $\\eta$ have mean 0, the data label's mean is captured by $\\mathbf{X}\\beta + \\alpha$. The random effects component $\\mathbf{Z}\\eta$ captures variations in the data: for example, \"Instructor \\#54 is rated 1.4 points higher than the mean.\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7B6ROTDQdTjH"
      },
      "source": [
        "In this tutorial, we posit the following effects:\n",
        "\n",
        "+ Fixed effects: `service`. `service` is a binary covariate corresponding to whether the course belongs to the instructor's main department. No matter how much additional data we collect, it can only take on values $0$ and $1$.\n",
        "+ Random effects: `students`, `instructors`, and `departments`. Given more observations from the population of course evaluation ratings, we may be looking at new students, teachers, or departments.\n",
        "\n",
        "In the syntax of R's lme4 package (Bates et al., 2015), the model can be summarized as\n",
        "\n",
        "```\n",
        "ratings ~ service + (1|students) + (1|instructors) + (1|departments) + 1\n",
        "```\n",
        "where `x` denotes a fixed effect,`(1|x)` denotes a random effect for `x`, and `1` denotes an intercept term.\n",
        "\n",
        "We implement this model below as a JointDistribution. To have better support for parameter tracking (e.g., we want to track all the `tf.Variable` in `model.trainable_variables`), we implement the model template as `tf.Module`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GS7SjqREp9wC"
      },
      "outputs": [],
      "source": [
        "class LinearMixedEffectModel(tf.Module):\n",
        "  def __init__(self):\n",
        "    # Set up fixed effects and other parameters.\n",
        "    # These are free parameters to be optimized in E-steps\n",
        "    self._intercept = tf.Variable(0., name=\"intercept\")            # alpha in eq\n",
        "    self._effect_service = tf.Variable(0., name=\"effect_service\")  #  beta in eq\n",
        "    self._stddev_students = tfp.util.TransformedVariable(\n",
        "        1., bijector=tfb.Exp(), name=\"stddev_students\")            # sigma in eq\n",
        "    self._stddev_instructors = tfp.util.TransformedVariable(\n",
        "        1., bijector=tfb.Exp(), name=\"stddev_instructors\")         # sigma in eq\n",
        "    self._stddev_departments = tfp.util.TransformedVariable(\n",
        "        1., bijector=tfb.Exp(), name=\"stddev_departments\")         # sigma in eq\n",
        "\n",
        "  def __call__(self, features):\n",
        "    model = tfd.JointDistributionSequential([\n",
        "      # Set up random effects.\n",
        "      tfd.MultivariateNormalDiag(\n",
        "          loc=tf.zeros(num_students),\n",
        "          scale_identity_multiplier=self._stddev_students),\n",
        "      tfd.MultivariateNormalDiag(\n",
        "          loc=tf.zeros(num_instructors),\n",
        "          scale_identity_multiplier=self._stddev_instructors),\n",
        "      tfd.MultivariateNormalDiag(\n",
        "          loc=tf.zeros(num_departments),\n",
        "          scale_identity_multiplier=self._stddev_departments),\n",
        "      # This is the likelihood for the observed.\n",
        "      lambda effect_departments, effect_instructors, effect_students: tfd.Independent(\n",
        "          tfd.Normal(\n",
        "              loc=(self._effect_service * features[\"service\"] +\n",
        "                  tf.gather(effect_students, features[\"students\"], axis=-1) +\n",
        "                  tf.gather(effect_instructors, features[\"instructors\"], axis=-1) +\n",
        "                  tf.gather(effect_departments, features[\"departments\"], axis=-1) +\n",
        "                  self._intercept),\n",
        "              scale=1.),\n",
        "              reinterpreted_batch_ndims=1)\n",
        "    ])\n",
        "\n",
        "    # To enable tracking of the trainable variables via the created distribution,\n",
        "    # we attach a reference to `self`. Since all TFP objects sub-class\n",
        "    # `tf.Module`, this means that the following is possible:\n",
        "    # LinearMixedEffectModel()(features_train).trainable_variables\n",
        "    # ==> tuple of all tf.Variables created by LinearMixedEffectModel.\n",
        "    model._to_track = self\n",
        "    return model\n",
        "\n",
        "lmm_jointdist = LinearMixedEffectModel()\n",
        "# Conditioned on feature/predictors from the training data\n",
        "lmm_train = lmm_jointdist(features_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WmaYmavUtpGh"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(<tf.Variable 'stddev_students:0' shape=() dtype=float32, numpy=0.0>,\n",
              " <tf.Variable 'stddev_instructors:0' shape=() dtype=float32, numpy=0.0>,\n",
              " <tf.Variable 'stddev_departments:0' shape=() dtype=float32, numpy=0.0>,\n",
              " <tf.Variable 'effect_service:0' shape=() dtype=float32, numpy=0.0>,\n",
              " <tf.Variable 'intercept:0' shape=() dtype=float32, numpy=0.0>)"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "lmm_train.trainable_variables"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3G_0t3jiZps2"
      },
      "source": [
        "As a Probabilistic graphical program, we can also visualize the model's structure in terms of its computational graph. This graph encodes dataflow across the random variables in the program, making explicit their relationships in terms of a graphical model (Jordan, 2003).\n",
        "\n",
        "As a statistical tool, we might look at the graph in order to better see, for example, that `intercept` and `effect_service` are conditionally dependent given `ratings`; this may be harder to see from the source code if the program is written with classes, cross references across modules, and/or subroutines. As a computational tool, we might also notice latent variables flow into the `ratings` variable via `tf.gather` ops. This may be a bottleneck on certain hardware accelerators if indexing `Tensor`s is expensive; visualizing the graph makes this readily apparent.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ox_kZeuOygqn"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(('effect_students', ()),\n",
              " ('effect_instructors', ()),\n",
              " ('effect_departments', ()),\n",
              " ('x', ('effect_departments', 'effect_instructors', 'effect_students')))"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "lmm_train.resolve_graph()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZPZTWsCeB7Va"
      },
      "source": [
        "## Parameter Estimation\n",
        "\n",
        "Given data, the goal of inference is to fit the model's fixed effects slope $\\beta$, intercept $\\alpha$, and variance component parameter $\\sigma^2$. The maximum likelihood principle formalizes this task as\n",
        "\n",
        "$$\n",
        "\\max_{\\beta, \\alpha, \\sigma}~\\log p(\\mathbf{y}\\mid \\mathbf{X}, \\mathbf{Z}; \\beta, \\alpha, \\sigma) = \\max_{\\beta, \\alpha, \\sigma}~\\log \\int p(\\eta; \\sigma) ~p(\\mathbf{y}\\mid \\mathbf{X}, \\mathbf{Z}, \\eta; \\beta, \\alpha)~d\\eta.\n",
        "$$\n",
        "\n",
        "In this tutorial, we use the Monte Carlo EM algorithm to maximize this marginal density (Dempster et al., 1977; Wei and Tanner, 1990).¹ We perform Markov chain Monte Carlo to compute the expectation of the conditional likelihood with respect to the random effects (\"E-step\"), and we perform gradient descent to maximize the expectation with respect to the parameters (\"M-step\"):\n",
        "\n",
        "+ For the E-step, we set up Hamiltonian Monte Carlo (HMC). It takes a current state—the student, instructor, and department effects—and returns a new state. We assign the new state to TensorFlow variables, which will denote the state of the HMC chain.\n",
        "\n",
        "+ For the M-step, we use the posterior sample from HMC to calculate an unbiased estimate of the marginal likelihood up to a constant. We then apply its gradient with respect to the parameters of interest. This produces an unbiased stochastic descent step on the marginal likelihood. We implement it with the Adam TensorFlow optimizer and minimize the negative of the marginal."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "U1Ro35iA7UPG"
      },
      "outputs": [],
      "source": [
        "target_log_prob_fn = lambda *x: lmm_train.log_prob(x + (labels_train,))\n",
        "trainable_variables = lmm_train.trainable_variables\n",
        "current_state = lmm_train.sample()[:-1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QQxq9acQ9MpO"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=float32, numpy=-528062.5>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# For debugging\n",
        "target_log_prob_fn(*current_state)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "F7uOcwQFB7Vb"
      },
      "outputs": [],
      "source": [
        "# Set up E-step (MCMC).\n",
        "hmc = tfp.mcmc.HamiltonianMonteCarlo(\n",
        "    target_log_prob_fn=target_log_prob_fn,\n",
        "    step_size=0.015,\n",
        "    num_leapfrog_steps=3)\n",
        "kernel_results = hmc.bootstrap_results(current_state)\n",
        "\n",
        "@tf.function(autograph=False, experimental_compile=True)\n",
        "def one_e_step(current_state, kernel_results):\n",
        "  next_state, next_kernel_results = hmc.one_step(\n",
        "      current_state=current_state,\n",
        "      previous_kernel_results=kernel_results)\n",
        "  return next_state, next_kernel_results\n",
        "\n",
        "optimizer = tf.optimizers.Adam(learning_rate=.01)\n",
        "\n",
        "# Set up M-step (gradient descent).\n",
        "@tf.function(autograph=False, experimental_compile=True)\n",
        "def one_m_step(current_state):\n",
        "  with tf.GradientTape() as tape:\n",
        "    loss = -target_log_prob_fn(*current_state)\n",
        "  grads = tape.gradient(loss, trainable_variables)\n",
        "  optimizer.apply_gradients(zip(grads, trainable_variables))\n",
        "  return loss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6BaHczzpkt0k"
      },
      "source": [
        "We perform a warm-up stage, which runs one MCMC chain for a number of iterations so that training may be initialized within the posterior's probability mass. We then run a training loop. It jointly runs the E and M-steps and records values during training."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XwZMt2uqVDzh"
      },
      "outputs": [],
      "source": [
        "num_warmup_iters = 1000\n",
        "num_iters = 1500\n",
        "num_accepted = 0\n",
        "effect_students_samples = np.zeros([num_iters, num_students])\n",
        "effect_instructors_samples = np.zeros([num_iters, num_instructors])\n",
        "effect_departments_samples = np.zeros([num_iters, num_departments])\n",
        "loss_history = np.zeros([num_iters])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zxbcYtrUt3OG"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Warm-Up Iteration:   0 Acceptance Rate: 1.000\n",
            "Warm-Up Iteration: 500 Acceptance Rate: 0.754\n",
            "Warm-Up Iteration: 999 Acceptance Rate: 0.707\n",
            "Iteration:    0 Acceptance Rate: 1.000 Loss: 98220.266\n",
            "Iteration:  500 Acceptance Rate: 0.703 Loss: 96003.969\n",
            "Iteration: 1000 Acceptance Rate: 0.678 Loss: 95958.609\n",
            "Iteration: 1499 Acceptance Rate: 0.685 Loss: 95921.891\n"
          ]
        }
      ],
      "source": [
        "# Run warm-up stage.\n",
        "for t in range(num_warmup_iters):\n",
        "  current_state, kernel_results = one_e_step(current_state, kernel_results)\n",
        "  num_accepted += kernel_results.is_accepted.numpy()\n",
        "  if t % 500 == 0 or t == num_warmup_iters - 1:\n",
        "    print(\"Warm-Up Iteration: {:>3} Acceptance Rate: {:.3f}\".format(\n",
        "        t, num_accepted / (t + 1)))\n",
        "\n",
        "num_accepted = 0  # reset acceptance rate counter\n",
        "\n",
        "# Run training.\n",
        "for t in range(num_iters):\n",
        "  # run 5 MCMC iterations before every joint EM update\n",
        "  for _ in range(5):\n",
        "    current_state, kernel_results = one_e_step(current_state, kernel_results)\n",
        "  loss = one_m_step(current_state)\n",
        "  effect_students_samples[t, :] = current_state[0].numpy()\n",
        "  effect_instructors_samples[t, :] = current_state[1].numpy()\n",
        "  effect_departments_samples[t, :] = current_state[2].numpy()\n",
        "  num_accepted += kernel_results.is_accepted.numpy()\n",
        "  loss_history[t] = loss.numpy()\n",
        "  if t % 500 == 0 or t == num_iters - 1:\n",
        "    print(\"Iteration: {:>4} Acceptance Rate: {:.3f} Loss: {:.3f}\".format(\n",
        "        t, num_accepted / (t + 1), loss_history[t]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gyo91h1oVx_L"
      },
      "source": [
        "You can also write the warmup for-loop into a `tf.while_loop`, and the training step into a `tf.scan` or `tf.while_loop` for even faster inference. For example:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9WmwCZNQWqh7"
      },
      "outputs": [],
      "source": [
        "@tf.function(autograph=False, experimental_compile=True)\n",
        "def run_k_e_steps(k, current_state, kernel_results):\n",
        "  _, next_state, next_kernel_results = tf.while_loop(\n",
        "      cond=lambda i, state, pkr: i < k,\n",
        "      body=lambda i, state, pkr: (i+1, *one_e_step(state, pkr)),\n",
        "      loop_vars=(tf.constant(0), current_state, kernel_results)\n",
        "  )\n",
        "  return next_state, next_kernel_results"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r6U2zkdbHj5z"
      },
      "source": [
        "Above, we did not run the algorithm until a convergence threshold was detected. To check whether training was sensible, we verify that the loss function indeed tends to converge over training iterations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HR4A6FLCwD7b"
      },
      "outputs": [
        {
          "data": {
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L2UIcst1wS2ND/gnrigEAAIBfIbDAPwwc2nj8dZF1dQAAAMCvEFjgF2xRMZ5jo7LMwkoA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SmIiopC/fr1cdttt6FZs2aWzxPoa8I5x+LFi7Fy5UokJSUhJCQEDRo0wN13342GDRsW2b+/KBTk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\nEREREZHJ+h+CTPJK41y3GgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 264,
              "width": 406
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(loss_history)\n",
        "plt.ylabel(r'Loss $-\\log$ $p(y\\mid\\mathbf{x})$')\n",
        "plt.xlabel('Iteration')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fz7FphO9LwVE"
      },
      "source": [
        "We also use a trace plot, which shows the Markov chain Monte Carlo algorithm's trajectory across specific latent dimensions. Below we see that specific instructor effects indeed meaningfully transition away from their initial state and explore the state space. The trace plot also indicates that the effects differ across instructors but with similar mixing behavior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_NvaIhgrvY9o"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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WQEV9lWYTxmLiOKyt41tklk5L24d4pMuzLWKEn29VOpeyBcyuK5uUDHPgSb/s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\nDjJpUSvQrOJ7PB5FYUOEDH2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lO0UYzZ987FYHfqueny4mY2qyqmnWCUeLERDIC4FqIUP8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\nS6hQEcbQdUwNgD2Tr8SZWImt9GU0EpARoaVXbdBo7hB7dwFnrPCvr72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UYY4D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fByCKsal4W3aX5TArzRX/ycQRhBVW05kGxWENddk5P5igVXgcB5F+raGC8dbYBCgWhKwO7B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\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ffRYfffQRoqOjMWPGDCQnJ2PXrl349NNPMXz4cGRkZASsTPzh67nIV19fjzfeeANGoxE2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\nUNtIdaajwgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 264,
              "width": 396
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "for i in range(7):\n",
        "  plt.plot(effect_instructors_samples[:, i])\n",
        "\n",
        "plt.legend([i for i in range(7)], loc='lower right')\n",
        "plt.ylabel('Instructor Effects')\n",
        "plt.xlabel('Iteration')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-xVCGWZoB7Vd"
      },
      "source": [
        "## Criticism\n",
        "\n",
        "Above, we fitted the model. We now look into criticizing its fit using data, which lets us explore and better understand the model. One such technique is a residual plot, which plots the difference between the model's predictions and ground truth for each data point. If the model were correct, then their difference should be standard normally distributed; any deviations from this pattern in the plot indicate model misfit.\n",
        "\n",
        "We build the residual plot by first forming the posterior predictive distribution over ratings, which replaces the prior distribution on the random effects with its posterior given training data. In particular, we run the model forward and intercept its dependence on prior random effects with their inferred posterior means.²"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p4vreJekB7Vf"
      },
      "outputs": [],
      "source": [
        "lmm_test = lmm_jointdist(features_test)\n",
        "\n",
        "[\n",
        "    effect_students_mean,\n",
        "    effect_instructors_mean,\n",
        "    effect_departments_mean,\n",
        "] = [\n",
        "     np.mean(x, axis=0).astype(np.float32) for x in [\n",
        "       effect_students_samples,\n",
        "       effect_instructors_samples,\n",
        "       effect_departments_samples\n",
        "       ]\n",
        "]\n",
        "\n",
        "# Get the posterior predictive distribution\n",
        "(*posterior_conditionals, ratings_posterior), _ = lmm_test.sample_distributions(\n",
        "    value=(\n",
        "        effect_students_mean,\n",
        "        effect_instructors_mean,\n",
        "        effect_departments_mean,\n",
        "))\n",
        "\n",
        "ratings_prediction = ratings_posterior.mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zTQJ3d-Hv93z"
      },
      "source": [
        "Upon visual inspection, the residuals look somewhat standard-normally distributed. However, the fit is not perfect: there is larger probability mass in the tails than a normal distribution, which indicates the model might improve its fit by relaxing its normality assumptions.\n",
        "\n",
        "In particular, although it is most common to use a normal distribution to model ratings in the `InstEval` data set, a closer look at the data reveals that course evaluation ratings are in fact ordinal values from 1 to 5. This suggests that we should be using an ordinal distribution, or even Categorical if we have enough data to throw away the relative ordering. This is a one-line change to the model above; the same inference code is applicable."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0jIxfwuvEWLG"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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CBbi4uJhdTu1jzJzXnmrSPAnnLQ8PD2RnZ+POnTuV/l0HSi5MNRfo+fn5iI2N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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 265,
              "width": 378
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.title(\"Residuals for Predicted Ratings on Test Set\")\n",
        "plt.xlim(-4, 4)\n",
        "plt.ylim(0, 800)\n",
        "plt.hist(ratings_prediction - labels_test, 75)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wi4hnI8UxFD2"
      },
      "source": [
        "To explore how the model makes individual predictions, we look at the histogram of effects for students, instructors, and departments. This lets us understand how individual elements in a data point's feature vector tends to influence the outcome.\n",
        "\n",
        "Not surprisingly, we see below that each student typically has little effect on an instructor's evaluation rating. Interestingly, we see that the department an instructor belongs to has a large effect."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MU-L604RFkxg"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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EdwAAAMAABHcAAADAAAR3AAAAwAAEdwAAAMAABHcAAADAAAR3AAAAwAC+7m4A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\nIibwP0GODNn0FdhWAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 265,
              "width": 375
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.title(\"Histogram of Student Effects\")\n",
        "plt.hist(effect_students_mean, 75)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "22qgTW7SGulD"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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rEcSBCuTYsWMF3ot88eLFtlnnYmJibPcwBwAArscAJaAC+eCDD7Rs2TL169dP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\nAHDB34oKSmqFIzXoAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 265,
              "width": 369
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.title(\"Histogram of Instructor Effects\")\n",
        "plt.hist(effect_instructors_mean, 75)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lTd2_uodGu2F"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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qAADgDYR6oA763e9+p6uvvlpffvml9u/fr/z8fP34449q0qSJOnbsqCFDhmj8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\nQ6CMVQWsAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 265,
              "width": 378
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.title(\"Histogram of Department Effects\")\n",
        "plt.hist(effect_departments_mean, 75)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ck3cPwIjvyqO"
      },
      "source": [
        "## Footnotes\n",
        "\n",
        "¹ Linear mixed effect models are a special case where we can analytically compute its marginal density. For the purposes of this tutorial, we demonstrate Monte Carlo EM, which more readily applies to non-analytic marginal densities such as if the likelihood were extended to be Categorical instead of Normal.\n",
        "\n",
        "² For simplicity, we form the predictive distribution's mean using only one forward pass of the model. This is done by conditioning on the posterior mean and is valid for linear mixed effects models. However, this is not valid in general: the posterior predictive distribution's mean is typically intractable and requires taking the empirical mean across multiple forward passes of the model given posterior samples."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8pm6qMKvB7WB"
      },
      "source": [
        "## Acknowledgments\n",
        "\n",
        "This tutorial was originally written in Edward 1.0 ([source](https://github.com/blei-lab/edward/blob/master/notebooks/linear_mixed_effects_models.ipynb)). We thank all contributors to writing and revising that version."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sHw7WpM1IzLO"
      },
      "source": [
        "## References\n",
        "\n",
        "1. Douglas Bates and Martin Machler and Ben Bolker and Steve Walker. Fitting Linear Mixed-Effects Models Using lme4. _Journal of Statistical Software_, 67(1):1-48, 2015.\n",
        "\n",
        "2. Arthur P. Dempster, Nan M. Laird, and Donald B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. _Journal of the Royal Statistical Society, Series B (Methodological)_, 1-38, 1977.\n",
        "\n",
        "3. Andrew Gelman and Jennifer Hill. _Data analysis using regression and multilevel/hierarchical models._ Cambridge University Press, 2006.\n",
        "\n",
        "4. David A. Harville. Maximum likelihood approaches to variance component estimation and to related problems. _Journal of the American Statistical Association_, 72(358):320-338, 1977.\n",
        "\n",
        "5. Michael I. Jordan. An Introduction to Graphical Models. Technical Report, 2003.\n",
        "\n",
        "6. Nan M. Laird and James Ware. Random-effects models for longitudinal data. _Biometrics_, 963-974, 1982.\n",
        "\n",
        "7. Greg Wei and Martin A. Tanner. A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. _Journal of the American Statistical Association_, 699-704, 1990."
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Linear_Mixed_Effects_Models.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
